Understanding Math Notation: Unions and Intersections Explained

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In summary, the notation \cup_{i\in I}A_{i} means that you take the union of a family of sets A_i, regardless of the size of the family. This is true for any set I and any open subsets A_i. Similarly, the notation \cap^{n}_{i=1}A_{i} means that you take the intersection of n sets, where A_i represents each individual set. This notation may differ from the traditional form of unions and intersections, which typically involve two sets.
  • #1
Oddbio
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In my math book, I am seeing a few things like this:

For any set I, and any family [itex](A_{i})_{i\in I}[/itex] of open subsets, the union [itex]\cup_{i\in I}A_{i}[/itex] is also an open set (any union of open sets is open);

I also see one later like:
[tex]\cap^{n}_{i=1}A_{i}[/tex]

But I always thought that a union (and intersection) had to be of the form:
[tex]A\cup B or A\cap B[/tex]

So the first one has nothing on the left side, same as the second one.. but the second one also has super and sub-scripts?
Do they mean something completely different than "union" and "intersection"?

I apologize if this is a trivial question.. it sure feels like it.
 
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  • #2
The notation of the form [itex]\cup_{i\in I}A_{i}[/itex], means that you have a family of sets A_i, and you do the union of all of them. i.e.,

[tex]\cup_{i\in I}A_{i} = A_1\cup A_2\cup...[/tex]
 
  • #3
Actually I guess that isn't strictly true, since the family of sets doesn't have to be countable, but I hope you get the idea.
 

1. What is mathematical notation?

Mathematical notation is a system of symbols and conventions used to represent mathematical equations and expressions. It is a standardized way of writing mathematical concepts and allows for clear and concise communication of mathematical ideas.

2. Why is mathematical notation important?

Mathematical notation is important because it allows for complex mathematical ideas and equations to be communicated in a concise and precise manner. It also allows for consistency and a universal understanding among mathematicians and scientists.

3. How do I read mathematical notation?

To read mathematical notation, start with the symbols and identify what they represent. Then, follow the order of operations to solve the equation or expression. It may also be helpful to refer to a mathematical notation guide for specific symbols and conventions.

4. What are some common symbols used in mathematical notation?

Some common symbols used in mathematical notation include numbers, variables, operators (such as +, -, x, /), parentheses, and equal signs. Other symbols may be used to represent specific mathematical functions or concepts.

5. How can I improve my understanding of mathematical notation?

To improve your understanding of mathematical notation, practice solving equations and expressions using different notation. It may also be helpful to study mathematical notation guides and seek help from a tutor or teacher if needed.

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